notes complete the square

Name: Date:

Algebra II HW Learning Target “I can solve quadratics by completing the square and writing in

vertex form.”

Notetaking Guide: Solving Quadratic equations by completing the square.

Warmup:

1. Solve (x 1)2  1 2. Factor x2  10x  25 3. Factor x2 16x  64

Completing the square: To complete the square for the expression

x2  b  2
 2 
 bx , add .

Example #1: Solve the quadratic equation by completing the square

x2 8x  9 Write original equation:

Write left side in the form x 2  bx

Add (____)2  (____)2  ___ to each side

Write the left side as a binomial squared

Take the square root of both sides

Solve for x

Simplify

The solutions are _____________ and ________________

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Example #2: Solve the following quadratic equation

x2  6x  4  0 Write original equation:

Write left side in the form x 2  bx

Add (____)2  (____)2  ___ to each side

Write the left side as a binomial squared

Take the square root of both sides

Solve for x

Simplify

The solutions are _____________ and ________________

Example #3: Solve the following quadratic equation

3x2 12x 18  0 Write original equation:

Write left side in the form x 2  bx

Add (____)2  (____)2  ___ to each side

Write the left side as a binomial squared
Take the square root of both sides
Solve for x
Simplify

The solutions are _____________ and ________________

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Example #4: Find the value of x.

Use the Area formula for a rectangle to determine x.
Write an expression for Area
Distributive property

Write one side in x 2  bx form

Add (____)2  ___ to each side

Write the left side as a binomial squared
Take the square root of both sides
Solve for x
Simplify
The value of x is _________________

Example #5: Write y  x2 10x  22 in vertex form. Then identify the vertex.

Write original equation
Prepare to complete the square

Add (____)2  ___ to each side

Write the right side as a binomial squared
Solve for y

The vertex form is _________________. The vertex is _____________

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Solve each equation by completing the square.

1. x2  2x  1  9 2. x 2  6x  9  25 3. x2 12x  36  18

4. x2  4x  5 5. x2  8x  12  0 6. x2  12x  20  0

7. x2 12x  3 8. x2  8x  4  0 9. x2  48  8x

10. x2  6x  10 11. x2  2x  5  0 12. x2  2x  20  0

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13. 6x2  12x  48 14. 5x2  20x  25  0 15. 3x2  3x  9  0

Write in vertex form and identify the vertex.

16. y  x2 16x  71 17. y  x2  4x 18. y  x2  6x  5

19. y  6  (x  3)2 20. y  6x2 12x 13 21. y  4x2  8x  20

1. x  4,2 2. x  2,8 3. x  6  2 2 4. x  5,1
5. x  2,6 6. x  2,10 7. x  6  39 8. x  4  2 3
9. x  4,12 10. x  3  i 11. x  1 2i 12. x  1  i 19
13. x  1  3 14. x  2  i 15. x 1 i 2 17. y  (x  8)2  7 vertex: (8,7)

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17. y  (x  2)2  4 vertex: (2,4) 18. y  (x  3)2  4 vertex: (3,4)
19. y  (x  3)2  6 vertex: (3,6) 20. y  6(x 1)2  7 vertex: (1,7)
21. y  4(x 1)2  24

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